Great Expectations

Finally, the men’s bracket at the Western and Southern Open tennis tournament stayed still long enough for me to model it. Here are the results:

This table is sorted by the player’s official world ranking, which is how the top 16 players in the bracket were initially seeded. While the ATP rank is obviously correlated with skill to some extent, it’s not the best available way to assess relative skill. For the purposes of the model, the primary indicator of skill is the odds offered on Betfair, a clearinghouse for sports wagering, on Friday night before the tourney started. ATP rank was the secondary sort, where the Betfair odds were equal, and for the qualifiers and lucky losers.

There are some biases in the Betfair odds. One is that there were no odds quoted for qualifiers and those who became lucky losers, so those folks all go to the bottom of the list, even though some of them would, no doubt, have been quoted at shorter odds if it had been known that they’d be in the main draw. There’s also a distinct bias in favor of Americans. John Isner has the eleventh best ATP ranking, but had the fourth shortest betting odds, presumably reflecting the assumption that he’d do particularly well in familiar surroundings in front of a supportive crowd.

Note that the simulation is for the bracket before any games had been played. Now, of course, the winnings of about half the field are known with certainty because they’ve already been eliminated – they earn $17,700 if they were eliminated in the first round, or $32,780 if eliminated in the second. The point here is not to predict anyone’s actual outcome, but rather to show how the peculiar practices of the ATP with regard to filling their brackets cause some odd anomalies.

Here’s a doozy. The seven qualifiers – Smith, Youzhny, Dolgopolov, Eubanks, Marterer Krueger, and Sousa – collectively can expect to earn $228,451. But the seven players they beat in the qualifying finals collectively expect $250,320! At it turned out, the qualifiers would have done better, on average, if they’d lost that last qualifying match, and taken their chances to be lucky losers.

ATP rank

skill rank

expected winnings

2

1

Nadal

$406,330

7

5

Thiem

$188,187

8

2

A. Zverev

$299,402

11

3

Dimitrov

$210,528

12

6

Tsonga

$132,150

13

16

Goffin

$45,745

14

9

Berdych

$70,493

15

21

Carreno Busta

$59,376

16

17

Bautista Agut

$77,293

17

10

Sock

$93,214

19

4

Isner

$133,810

20

11

Querrey

$89,295

21

12

Muller

$65,476

23

43

Ramon-Vinolas

$36,025

24

7

Kyrgios

$81,424

25

29

Fognini

$40,113

26

18

M. Zverev

$62,326

28

13

Lopez

$49,956

29

22

Gasquet

$40,320

30

30

Khachanov

$50,040

31

8

Del Potro

$77,684

32

20

Anderson

$48,741

33

33

Ferrer

$46,834

34

14

Karlovic

$52,000

35

23

Johnson

$59,975

36

31

Schwartzman

$49,237

38

36

Lorenzi

$41,225

40

24

Verdasco

$50,870

41

34

Paire

$40,124

42

44

Mannarino

$37,756

43

19

Edmund

$62,351

44

32

R. Harrison

$35,599

45

25

Troicki

$35,698

46

37

Sugita

$36,939

48

26

Medvedev

$42,822

49

27

Vesely

$35,080

51

45

Sousa

$35,438

52

35

Hasse

$43,339

55

38

Coric

$48,818

56

15

Chung

$45,213

58

46

Tipsarevic

$66,079

61

28

Young

$41,244

63

39

Basilashvili

$48,026

66

40

Donaldson

$42,145

71

47

Dolgopolov

$30,743

84

41

Tiafoe

$33,803

85

48

Fabbiano

$64,448

98

49

Youzhny

$33,813

122

50

Marterer

$30,747

132

51

Koslov

$32,045

174

42

Paul

$33,135

180

52

Ramanathan

$41,403

212

53

Smith

$26,854

240

54

C. Harrison

$66,150

244

55

Krueger

$31,285

374

56

Eubanks

$39,580

There’s more to be said about these results, but that will have to wait for tomorrow.